Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a small bowl, combine ground flaxseed meal and water; let sit for 5 minutes to thicken.
In a medium bowl, whisk together flour, baking soda, and salt.
In a large bowl, cream together softened vegan butter, peanut butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the flax egg and vanilla extract.
Gradually mix the dry ingredients into the wet ingredients until a cohesive dough forms.
Shape the dough into 1-inch balls and roll each ball in additional granulated sugar to coat.
Place balls 2 inches apart on the prepared baking sheet.
Bake for 8 to 10 minutes until edges are set but centers remain soft.
Immediately remove from oven and press one dairy-free chocolate piece into the center of each cookie, allowing it to crack slightly at the edges.
Transfer cookies to a wire rack to cool completely until the chocolate has set.